Assume that under specific conditions, hydrogen atoms are permitted to undergo only those transitions where the principal quantum number n changes by 2 . Determine the smallest wavelength emitted by hydrogen.

Step-by-step solution

The wavelength of the emitted photon is given by the Rydberg formula: 1 = R ( 1 n₁^2 - 1 n₂^2 ) For the smallest wavelength, the energy difference between the transition levels must be maximum. Given the condition that the principal quantum number changes by 2 , we have n₂ - n₁ = 2 . The maximum energy difference occurs for the lowest possible values of n₁ and n₂ . Thus, the transition is from n₂ = 3 to n₁ = 1 . Substituting these values into the formula: 1 = R ( 1 1^2 - 1 3^2 ) = R ( 1 - 1 9 ) = 8R 9 = 9 8R Using